A real-space, rela-time method for the dielectric function

We present an algorithm to calculate the linear response of periodic systems in the time-dependent density functional thoery, using a real-space representation of the electron wave functions and calculating the dynamics in real time. The real-space formulation increases the efficiency for calculating the interaction, and the real-time treatment decreases storage requirements and the allows the entire frequency-dependent response to be calculated at once. We give as examples the dielectric functions of a simple metal, lithium, and an elemental insulator, diamond.Comment: 17 pages, Latex, 5 figure

Model for nucleation in GaAs homoepitaxy derived from first principles

The initial steps of MBE growth of GaAs on beta 2-reconstructed GaAs(001) are investigated by performing total energy and electronic structure calculations using density functional theory and a repeated slab model of the surface. We study the interaction and clustering of adsorbed Ga atoms and the adsorption of As_2 molecules onto Ga atom clusters adsorbed on the surface. The stable nuclei consist of bound pairs of Ga adatoms, which originate either from dimerization or from an indirect interaction mediated through the substrate reconstruction. As_2 adsorption is found to be strongly exothermic on sites with a square array of four Ga dangling bonds. Comparing two scenarios where the first As_2 gets incorporated in the incomplete surface layer, or alternatively in a new added layer, we find the first scenario to be preferable. In summary, the calculations suggest that nucleation of a new atomic layer is most likely on top of those surface regions where a partial filling of trenches in the surface has occurred before.Comment: 8 pages, 14 figures, Submitted to Phys. Rev. B (December 15, 1998). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Scenario planning for the Edinburgh city region

This paper examines the application of scenario planning techniques to the detailed and daunting challenge of city re-positioning when policy makers are faced with a heavy history and a complex future context. It reviews a process of scenario planning undertaken in the Edinburgh city region, exploring the scenario process and its contribution to strategies and policies for city repositioning. Strongly rooted in the recent literature on urban and regional economic development, the text outlines how key individuals and organisations involved in the process participated in far-reaching analyses of the possible future worlds in which the Edinburgh city region might find itself

Broken-symmetry-adapted Green function theory of condensed matter systems:towards a vector spin-density-functional theory

The group theory framework developed by Fukutome for a systematic analysis of the various broken symmetry types of Hartree-Fock solutions exhibiting spin structures is here extended to the general many body context using spinor-Green function formalism for describing magnetic systems. Consequences of this theory are discussed for examining the magnetism of itinerant electrons in nanometric systems of current interest as well as bulk systems where a vector spin-density form is required, by specializing our work to spin-density-functional formalism. We also formulate the linear response theory for such a system and compare and contrast them with the recent results obtained for localized electron systems. The various phenomenological treatments of itinerant magnetic systems are here unified in this group-theoretical description.Comment: 17 page

A search for ferromagnetism in transition-metal-doped piezoelectric ZnO

We present the results of a computational study of ZnO in the presence of Co and Mn substitutional impurities. The goal of our work is to identify potential ferromagnetic ground states within the (Zn,Co)O or (Zn,Mn)O material systems that are also good candidates for piezoelectricity. We find that, in contrast to previous results, robust ferromagnetism is not obtained by substitution of Co or Mn on the Zn site, unless additional carriers (holes) are also incorporated. We propose a practical scheme for achieving such $p$-type doping in ZnO

Towards unified understanding of conductance of stretched monatomic contacts

When monatomic contacts are stretched, their conductance behaves in qualitatively different ways depending on their constituent atomic elements. Under a single assumption of resonance formation, we show that various conductance behavior can be understood in a unified way in terms of the response of the resonance to stretching. This analysis clarifies the crucial roles played by the number of valence electrons, charge neutrality, and orbital shapes.Comment: 2 figure

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices